Vol. 285, No. 2, 2016

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ISSN: 0030-8730
Conformal holonomy equals ambient holonomy

Andreas Čap, A. Rod Gover, C. Robin Graham and Matthias Hammerl

Vol. 285 (2016), No. 2, 303–318
Abstract

We study the relation between two notions of holonomy on a conformal manifold. The first is the conformal holonomy, defined to be the holonomy of the normal tractor connection. The second is the holonomy of the Fefferman–Graham ambient metric of the conformal manifold. It is shown that the infinitesimal conformal holonomy and the infinitesimal ambient holonomy always agree up to the order that the ambient metric is defined.

Keywords
holonomy, ambient metric, tractor, conformal geometry
Mathematical Subject Classification 2010
Primary: 53A30
Secondary: 53C29
Milestones
Received: 3 April 2015
Revised: 9 March 2016
Accepted: 8 June 2016
Published: 21 November 2016
Authors
Andreas Čap
Faculty of Mathematics
University of Vienna
Oskar-Morgenstern-Platz 1
1090 Wien
Austria
A. Rod Gover
Department of Mathematics
The University of Auckland
Private Bag 92019
Auckland 1142
New Zealand
C. Robin Graham
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350
United States
Matthias Hammerl
Department of Mathematics and Informatics
University of Greifswald
Walther-Rathenau-Str. 47
D-17489 Greifswald
Germany